Do you know what is the difference between Cleanse and Clean? I don't have a clear idea of when to use one or the other as verbs or nouns, or if there is some key difference I'm not aware of.
They are very similar in meaning, but as a rule, Cleanse has a sense of a more thorough or radical clean. So, for example, I might clean my mug by washing it up, but I might get it cleansed by chemical treatments, boiling water or whatever. It is a more thorough sense of dirt removal — a deep clean, if you want.
So in this term, Ethnic Cleansing is about a rooting out of all aspects of the ethnic group being cleansed. Colonic cleansing is (I am guessing, not ever having had or wanted it) removal of all the colonic gunge, not just a wipe down.
Similarly, you might clear your desk with a cloth, but a cleansing — to remove years of ingrained dirt — would probably involve steam cleaning.
Which to use? It very much depends on the context. Cleansing does have some negative connotations, so some care should be used.
'Cleanse' is an old word, going back to OE. 'Clean' is a newer word that appeared in the 15th century and largely displaced 'cleanse'.
The result of the displacement is that 'clean' is now used in literal applications of removing dirt, and 'cleanse' has retreated into figurative use, such as the ethnic cleansing or spiritual cleansing that Matt mentions in comments.
These two words are really equivalent.
I think you'll find that clean is used more commonly. For the most part, cleanse would be considered a little more old fashioned or technical, depending on the context.
Edit: From reference.dictionary.com:
Clean, cleanse refer to removing dirt or impurities. To clean is the general word with no implication of method or means: to clean windows, a kitchen, streets. Cleanse is especially used of thorough cleaning by chemical or other technical process; figuratively it applies to moral or spiritual purification: to cleanse parts of machinery; to cleanse one's soul of guilt.